XII. Dialectics.
Quantity and Quality

“The first and most important principle of the basic
logical properties of being refers to the exclusion of contradiction.
Contradiction is a category which can only appertain to a combination of
thoughts, but not to reality. There are no contradictions in things, or, to put
it another way, contradiction accepted as reality is itself the apex of
absurdity {D. Ph. 30} ... The antagonism of forces measured against each other
and moving in opposite directions is in fact the basic form of all actions m
the life of the world and its creatures. But this opposition of the directions
taken by the forces of elements and individuals does not in the slightest
degree coincide with the idea of absurd contradictions {31} ... We can be
content here with having cleared the fogs which generally rise from the
supposed mysteries of logic by presenting a clear picture of the actual
absurdity of contradictions in reality and with having shown the uselessness of
the incense which has been burnt here and there in honour of the dialectics of
contradiction — the very clumsily carved wooden doll which is substituted
for the antagonistic world schematism” {32}

This is practically all we are told about dialectics in the
Cursus der Philosophie. In his Kritische Geschichte, on the
other hand, the dialectics of contradiction, and with it particularly Hegel, is
treated quite differently.

“Contradiction, according to the Hegelian logic, or
rather Logos doctrine, is objectively present not in thought, which by its
nature can only be conceived as subjective and conscious, but in things and
processes themselves and can be met with in so to speak corporeal form, so that
absurdity does not remain an impossible combination of thought but becomes an
actual force. The reality of the absurd is the first article of faith in the
Hegelian unity of the logical and the illogical.... The more contradictory a
thing the truer it is, or in other words, the more absurd the more credible it
is. This maxim, which is not even newly invented but is borrowed from the
theology of the Revelation and from mysticism, is the naked expression of the
so-called dialectical principle” {D. K. G. 479-80}.

The thought-content of the two passages cited can be summed up
in the statement that contradiction=absurdity, and therefore cannot occur in
the real world. People who in other respects show a fair degree of common sense
may regard this statement as having the same self-evident validity as the
statement that a straight line cannot be a curve and a curve cannot be
straight. But, regardless of all protests made by common sense, the
differential calculus under certain circumstances nevertheless equates straight
lines and curves, and thus obtains results which common sense, insisting on the
absurdity of straight lines being identical with curves, can never attain. And
in view of the important role which the so-called dialectics of contradiction
has played in philosophy from the time of the ancient Greeks up to the present,
even a stronger opponent than Herr Dühring should have felt obliged to attack
it with other arguments besides one assertion and a good many abusive
epithets.

True, so long as we consider things as at rest and lifeless, each one by
itself, alongside and after each other, we do not run up against any
contradictions in them. We find certain qualities which are partly common to,
partly different from, and even contradictory to each other, but which in the
last-mentioned case are distributed among different objects and therefore
contain no contradiction within. Inside the limits of this sphere of
observation we can get along on the basis of the usual, metaphysical mode of
thought. But the position is quite different as soon as we consider things in
their motion, their change, their life, their reciprocal influence on one
another. Then we immediately become involved in contradictions. Motion itself
is a contradiction: even simple mechanical change of position can only come
about through a body being at one and the same moment of time both in one place
and in another place, being in one and the same place and also not in it. And
the continuous origination and simultaneous solution of this contradiction is
precisely what motion is.

Here, therefore, we have a contradiction which “is objectively present
in things and processes themselves and can be met with in so to speak corporeal
form”. And what has Herr Dühring to say about it? He asserts that

up to the present there is “no bridge” whatever
“in rational mechanics from the strictly static to the dynamic” {D.
Ph. 80}.

The reader can now at last see what is hidden behind this
favourite phrase of Herr Dühring’s — it is nothing but this: the
mind which thinks metaphysically is absolutely unable to pass from the idea of
rest to the idea of motion, because the contradiction pointed out above blocks
its path. To it, motion is simply incomprehensible because it is a
contradiction. And in asserting the incomprehensibility of motion, it admits
against its will the existence of this contradiction, and thus admits the
objective presence in things and processes themselves of a contradiction which
is moreover an actual force.

If simple mechanical change of position contains a contradiction this is
even more true of the higher forms of motion of matter, and especially of
organic life and its development. We saw above that life consists precisely and
primarily in this — that a being is at each moment itself and yet
something else. Life is therefore also a contradiction which is present in
things and processes themselves, and which constantly originates and resolves
itself; and as soon as the contradiction ceases, life, too, comes to an end,
and death steps in. We likewise saw that also in the sphere of thought we could
not escape contradictions, and that for example the contradiction between man's
inherently unlimited capacity for knowledge and its actual presence only in men
who are externally limited and possess limited cognition finds its solution in
what is — at least practically, for us — an endless succession of
generations, in infinite progress.

We have already noted that one of the basic principles of higher mathematics
is the contradiction that in certain circumstances straight lines and curves
may be the same. It also gets up this other contradiction: that lines which
intersect each other before our eyes nevertheless, only five or six centimetres
from their point of intersection, can be shown to be parallel, that is, that
they will never meet even if extended to infinity. And yet, working with these
and with even far greater contradictions, it attains results which are not only
correct but also quite unattainable for lower mathematics.

But even lower mathematics teems with contradictions. It is for example a
contradiction that a root of A should be a power of A, and yet A1/2
= . It is a contradiction that a
negative quantity should be the square of anything, for every negative quantity
multiplied by itself gives a positive square. The square root of minus one is
therefore not only a contradiction, but even an absurd contradiction, a real
absurdity. And yet is in
many cases a necessary result of correct mathematical operations. Furthermore,
where would mathematics — lower or higher — be, if it were
prohibited from operation with ?

In its operations with variable quantities mathematics itself enters the
field of dialectics, and it is significant that it was a dialectical
philosopher, Descartes, who introduced this advance. The relation between the
mathematics of variable and the mathematics of constant quantities is in
general the same as the relation of dialectical to metaphysical thought. But
this does not prevent the great mass of mathematicians from recognising
dialectics only in the sphere of mathematics, and a good many of them from
continuing to work in the old, limited, metaphysical way with methods that were
obtained dialectically.

It would be possible to go more closely into Herr Dühring’s antagonism
of forces and his antagonistic world schematism only if he had given us
something more on this theme than the mere phrase. After accomplishing
this feat this antagonism is not even once shown to us at work, either in his
world schematism or in his natural philosophy — the most convincing
admission that Herr Dühring can do absolutely nothing of a positive character
with his “basic form of all actions in the life of the world and its
creatures”. When someone has in fact lowered Hegel’s
“Doctrine of Essence” to the platitude of forces moving in opposite
directions but not in contradictions, certainly the best thing he can do is to
avoid any application of this commonplace.

Marx's Capital furnishes Herr Dühring with another occasion for
venting his anti-dialectical spleen.

“The absence of natural and intelligible logic which
characterises these dialectical frills and mazes and conceptual arabesques...
Even to the part that has already appeared we must apply the principle that in
a certain respect and also in general” (!), “according to a
well-known philosophical preconception, all is to be sought in each and each in
all, and that therefore, according to this mixed and misconceived idea, it all
amounts to one and the same thing in the end” {D. K. G. 496}.

This insight into the well-known philosophical preconception
also enables Herr Dühring to prophesy with assurance what will be the
“end” of Marx's economic philosophising, that is, what the
following volumes of Capital will contain, and this he does exactly
seven lines after he has declared that

“speaking in plain human language it is really
impossible to divine what is still to come in the two” (final)
“volumes” [61] {496}.

This, however, is not the first time that Herr Dühring’s
writings are revealed to us as belonging to the “things” in which
“contradiction is objectively present and can be
met with in so to speak corporeal form” {479-80}. But this does
not prevent him from going on victoriously as follows:

“Yet sound logic will in all probability triumph over
its caricature... This presence of superiority and this mysterious dialectical
rubbish will tempt no one who has even a modicum of sound judgment left to have
anything to do ... with these deformities of thought and style. With the demise
of the last relics of the dialectical follies this means of duping ... will
lose its deceptive influence, and no one will any longer believe that he has to
torture himself in order to get behind some profound piece of wisdom where the
husked kernel of the abstruse things reveals at best the features of ordinary
theories if not of absolute commonplaces... It is quite impossible to reproduce
the” (Marxian) “maze in accordance with the Logos doctrine without
prostituting sound logic” {D. K. C. 497}. Marx's method, according to
Herr Dühring, consists in “performing dialectical miracles for his
faithful followers” {498}, and so on.

We are not in any way concerned here as yet with the correctness
or incorrectness of the economic results of Marx's researches, but only with
the dialectical method used by Marx. But this much is certain: most readers of
Capital will have learnt for the first time from Herr Dühring what it
is in fact that they have read. And among them will also be Herr Dühring
himself, who in the year 1867 (Ergänzungsblätter III, No. 3) was still
able to provide what for a thinker of his calibre was a relatively rational
review of the book; and he did this without first being obliged as he now
declares is indispensable, to translate the Marxian argument into Dühringian
language. And though even then he committed the blunder of identifying Marxian
dialectics with the Hegelian, he had not quite lost the capacity to distinguish
between the method and the results obtained by using it, and to understand that
the latter are not refuted in detail by lampooning the former in general.

At any rate, the most astonishing piece of information given by Herr Dühring
is the statement that from the Marxian standpoint “it all amounts to one
and the same thing in the end” {496}, that therefore to Marx, for
example, capitalists and wage-workers, feudal, capitalist and socialist modes
of production are also “one and the same
thing” — no doubt in the end even Marx and Herr Dühring are
“one and the same thing”. Such utter nonsense can only be explained
if we suppose that the mere mention of the word dialectics throws Herr Dühring
into such a state of mental irresponsibility that, as a result of a certain
mixed and misconceived idea, what he says and does is “one and the same
thing” in the end.

We have here a sample of what Herr Dühring calls

“my historical depiction in the grand style”
{556}, or “the summary treatment which settles with genus and type, and
does not condescend to honour what a Hume called the learned mob with an
exposure in micrological detail; this treatment in a higher and nobler style is
the only one compatible with the interests of complete truth and with one's
duty to the public which is free from the bonds of the guilds” {507}.

Historical depiction in the grand style and the summary
settlement with genus and type is indeed very convenient for Herr Dühring,
inasmuch as this method enables him to neglect all known facts as micrological
and equate them to zero, so that instead of proving anything he need only use
general phrases, make assertions and thunder his denunciations. The method has
the further advantage that it offers no real foothold to an opponent, who is
consequently left with almost no other possibility of reply than to make
similar summary assertions in the grand style, to resort to general phrases and
finally thunder back denunciations at Herr Dühring — in a word, as they
say, engage in a clanging match, which is not to everyone“s taste. We
must therefore be grateful to Herr Dühring for occasionally, by way of
exception, dropping the higher and nobler style, and giving us at least two
examples of the unsound Marxian Logos doctrine.

“How comical is the reference to the confused, hazy
Hegelian notion that quantity changes into quality, and that therefore an
advance, when it reaches a certain size, becomes capital by this quantitative
increase alone” {498}.

In this “expurgated” presentation by Herr Dühring
that statement certainly seems curious enough. Let us see how it looks in the
original, in Marx. On page 313 (2nd edition of Capital), Marx, on the
basis of his previous examination of constant and variable capital and
surplus-value, draws the conclusion that “not every sum of money, or of
value, is at pleasure transformable into capital. To effect this
transformation, in fact, a certain minimum of money or of exchange-value must
be presupposed in the hands of the individual possessor of money or
commodities.” He takes as an example the case of a labourer in any branch
of industry, who works daily eight hours for himself — that is, in
producing the value of his wages — and the following four hours for the
capitalist, in producing surplus-value, which immediately flows into the pocket
of the capitalist. In this case, one would have to have at his disposal a sum
of values sufficient to enable one to provide two labourers with raw materials,
instruments of labour and wages, in order to pocket enough surplus-value every
day to live on as well as one of his labourers. And as the aim of capitalist
production is not mere subsistence but the increase of wealth, our man with his
two labourers would still not be a capitalist. Now in order that he may live
twice as well as an ordinary labourer, and turn half of the surplus-value
produced again into capital, he would have to be able to employ eight
labourers, that is, he would have to possess four times the sum of values
assumed above. And it is only after this, and in the course of still further
explanations elucidating and substantiating the fact that not every petty sum
of values is enough to be transformable into capital, but that in this respect
each period of development and each branch of industry has its definite minimum
sum, that Marx observes: “Here, as in natural science, is shown
the correctness of the law discovered by Hegel in his Logic, that
merely quantitative changes beyond a certain point pass into qualitative
differences.”

And now let the reader admire the higher and nobler style, by virtue of
which Herr Dühring attributes to Marx the opposite of what he really said. Marx
says: The fact that a sum of values can be transformed into capital only when
it has reached a certain size, varying according to the circumstances, but in
each case definite minimum size — this fact is a proof of the
correctness of the Hegelian law. Herr Dühring makes him say:
Because, according to the Hegelian law, quantity changes into quality,
“therefore an advance, when it reaches a
certain size, becomes capital” {D. K. G. 498}. That is to say, the
very opposite.

In connection with Herr Dühring’s examination of the Darwin case, we
have already got to know his habit, “in the
interests of complete truth” and because of his “duty to the public
which is free from the bonds of the guilds” {507}, of quoting
incorrectly. It becomes more and more evident that this habit is an inner
necessity of the philosophy of reality, and it is certainly a very “summary treatment” {507}. Not to mention
the fact that Herr Dühring further makes Marx speak of any kind of
“advance” whatsoever, whereas Marx only refers to an advance made
in the form of raw materials, instruments of labour, and wages; and that in
doing this Herr Dühring succeeds in making Marx speak pure nonsense. And then
he has the cheek to describe as comic the nonsense which he himself
has fabricated. Just as he built up a Darwin of his own fantasy in order to try
out his strength against him, so here he builds up a fantastic Marx. “Historical depiction in the grand style”
{556}, indeed!

We have already seen earlier, when discussing world schematism, that in
connection with this Hegelian nodal line of measure relations — in which
quantitative change suddenly passes at certain points into qualitative
transformation — Herr Dühring had a little accident: in a weak moment he
himself recognised and made use of this line. We gave there one of the
best-known examples — that of the change of the aggregate states of
water, which under normal atmospheric pressure changes at 0° C from the liquid
into the solid state, and at 100°C from the liquid into the gaseous state, so
that at both these turning-points the merely quantitative change of temperature
brings about a qualitative change in the condition of the water.

In proof of this law we might have cited hundreds of other similar facts
from nature as well as from human society. Thus, for example, the whole of Part
IV of Marx's Capital — production of relative surplus-value
— deals, in the field of co-operation, division of labour and
manufacture, machinery and modern industry, with innumerable cases in which
quantitative change alters the quality, and also qualitative change alters the
quantity, of the things under consideration; in which therefore, to use the
expression so hated by Herr Dühring, quantity is transformed into quality and
vice versa. As for example the fact that the co-operation of a number of
people, the fusion of many forces into one single force, creates, to use Marx's
phrase, a “new power”, which is essentially different from the sum
of its separate forces.

Over and above this, in the passage which, in the interests of complete
truth, Herr Dühring perverted into its opposite, Marx had added a footnote:
“The molecular theory of modern chemistry first scientifically worked out
by Laurent and Gerhardt rests on no other law.” But what did that matter
to Herr Dühring? He knew that:

“the eminently modern educative elements provided by
the natural-scientific mode of thought are lacking precisely among those who,
like Marx and his rival Lassalle, make half-science and a little
philosophistics the meagre equipment with which to vamp up their
learning” {D. K. G. 504} —

while with Herr Dühring

“the main achievements of exact knowledge in mechanics,
physics and chemistry” {D. Ph. 517} and so forth serve as the basis
—

we have seen how. However, in order to enable third persons,
too, to reach a decision in the matter, we shall look a little more closely
into the example cited in Marx's footnote.

What is referred to here is the homologous series of carbon compounds, of
which a great many are already known and each of which has its own algebraic
formula of composition. If, for example, as is done in chemistry, we denote an
atom of carbon by C, an atom of hydrogen by H, an atom of oxygen by O, and the
number of atoms of carbon contained in each compound by n, the molecular
formulas for some of these series can be expressed as follows:

CnH2n+2 — the series of normal
paraffins
CnH2n+2O — the series of primary alcohols
CnH2nO2 — the series of the monobasic
fatty acids.

Let us take as an example the last of these series, and let us
assume successively that n=l, n=2, n=3, etc. We then obtain the following
results (omitting the isomers):

and so on to C50H60O2, melissic
acid, which melts only at 80° and has no boiling point at all, because it
cannot evaporate without disintegrating.

Here therefore we have a whole series of qualitatively different bodies,
formed by the simple quantitative addition of elements, and in fact always in
the same proportion. This is most clearly evident in cases where the quantity
of all the elements of the compound changes in the same proportion. Thus, in
the normal paraffins CnH2n+2, the lowest is methane, CH4,
a gas; the highest known, hexadecane, C16H34, is a solid
body forming colourless crystals which melts at 21° and boils only at 278°.
Each new member of both series comes into existence through the addition of
CH2, one atom of carbon and two atoms of hydrogen, to the molecular formula of
the preceding member, and this quantitative change in the molecular formula
produces each time a qualitatively different body.

These series, however, are only one particularly obvious example; throughout
practically the whole of chemistry, even in the various nitrogen oxides and
oxygen acids of phosphorus or sulphur, one can see how “quantity changes into
quality”, and this allegedly confused, hazy Hegelian notion appears in so to
speak corporeal form in things and processes — and no one but Herr
Dühring is confused and befogged by it. And if Marx was the first to call
attention to it, and if Herr Dühring read the reference without even
understanding it (otherwise he would certainly not have allowed this
unparalleled outrage to pass unchallenged), this is enough — even without
looking back at the famous Dühringian philosophy of nature — to make it
clear which of the two, Marx or Herr Dühring, is lacking in “the eminently modern educative elements provided by the
natural-scientific mode of thought” {D. K. G. 504} and in acquaintance
with the “main achievements of ... chemistry” {D.
Ph. 517}.

In conclusion we shall call one more witness for the transformation of
quantity into quality, namely — Napoleon. He describes the combat between
the French cavalry, who were bad riders but disciplined, and the Mamelukes, who
were undoubtedly the best horsemen of their time for single combat, but lacked
discipline, as follows:

“Two Mamelukes were undoubtedly more than a match for three
Frenchmen; 100 Mamelukes were equal to 100 Frenchmen; 300 Frenchmen could
generally beat 300 Mamelukes, and 1,000 Frenchmen invariably defeated 1,500
Mamelukes.”

Just as with Marx a definite, though varying, minimum sum of
exchange-values was necessary to make possible its transformation into capital,
so with Napoleon a detachment of cavalry had to be of a definite minimum number
in order to make it possible for the force of discipline, embodied in closed
order and planned utilisation, to manifest itself and rise superior even to
greater numbers of irregular cavalry, in spite of the latter being better
mounted, more dexterous horsemen and fighters, and at least as brave as the
former. But what does this prove as against Herr Dühring? Was not Napoleon
miserably vanquished in his conflict with Europe? Did he not suffer defeat
after defeat? And why? Solely in consequence of having introduced the confused,
hazy Hegelian notion into cavalry tactics!